论文标题
$ \ ell_p $空间和$ \ ell_p $产品空间中的几个距离集
Few distance sets in $\ell_p$ spaces and $\ell_p$ product spaces
论文作者
论文摘要
Kusner询问$ n+1 $点是否是$ \ Mathbb {r}^n $中的最大点数，以使任何两个点之间的$ \ ell_p $ dance $（1 <p <\ infty）$是$ 1 $。当$ n $而言，当$ p $较大时，我们对最著名的上限进行了改进，以及对$ s $ distance set的概括。我们还在欧几里得空间的$ \ ell_p $总和中研究等边组，在$ p = \ infty $，$ p $时，以等值设置的大小衍生出上限，均匀，任何$ 1 \ le le p <\ f <\ infty $。
Kusner asked if $n+1$ points is the maximum number of points in $\mathbb{R}^n$ such that the $\ell_p$ distance $(1<p<\infty)$ between any two points is $1$. We present an improvement to the best known upper bound when $p$ is large in terms of $n$, as well as a generalization of the bound to $s$-distance sets. We also study equilateral sets in the $\ell_p$ sums of Euclidean spaces, deriving upper bounds on the size of an equilateral set for when $p=\infty$, $p$ is even, and for any $1\le p<\infty$.
